Abstract
We have studied thermal chaotic behavior in the extended phase space for a charged dilaton-AdS black hole by Melnikov method and present the effect of dilaton parameter on the thermal chaos. Our result show that for the temporal perturbation the thermal chaos in the charged dilaton-AdS black hole occurs only if the perturbation amplitude is larger than certain a critical value, but for the spatially perturbation, the chaos always exists irrespective of perturbation amplitude. These behaviors are similar to those in other AdS black hole, which can be regarded as the common features of the static AdS black holes. Moreover, we also find that the critical temporal perturbation amplitude leading to chaos increases with the dilaton parameter and decreases with the charge. This means that under the temporal perturbation the presence of dilaton parameter makes the onset of chaos more difficult, which differs from that of the charge parameter.
Highlights
Chaos is a kind of very complicated and irregular motion, which appears only in the non-linear and non-integrable dynamical systems
It is shown that for the temporal perturbation the thermal chaos occurs only if the perturbation amplitude is larger than certain a critical value, but for the spatially perturbation, the chaos always exists irrespective of perturbation amplitude
We have studied thermal chaotic behavior in the extended phase space of a charged dilaton-AdS black hole by Melnikov method and present the effect of dilaton parameter on the thermal chaos
Summary
Chaos is a kind of very complicated and irregular motion, which appears only in the non-linear and non-integrable dynamical systems. It is very natural to probe the thermal chaos in AdS black holes with phase structures similar to that of van-der Waals fluid. We will study thermal chaos in the extended phase space for a charged dilaton-AdS black hole, which belongs to a family of solutions in Einstein–Maxwell-dilaton gravity theory [32,33,34]. The main purpose of this paper is to study thermal chaos of a charged dilaton-AdS black hole [32] and to probe the effects of dilaton parameter on thermal chaotic behaviors. 2, we will review briefly thermodynamics of a charged dilaton-AdS black hole [32] in the extended phase space and dependence of the critical temperature Tc on black hole parameters.
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